Flowability of modified magnesium slag-fly ash cemented coal gangue slurry in industrial loop-pipe tests

Abstract

Industrial-grade loop tests were conducted on modified backfill slurry (a slurry prepared with a modified magnesium slag-fly ash binder and coal gangue aggregate) across mass concentrations (64–72%) and flow rates (1.0–2.7 m/s) to analyze pipeline transportation characteristics. Results demonstrate that pressure loss increases linearly with flow rate, confirming Bingham plastic behavior, while exhibiting a nonlinear relationship with mass concentration. Critically, elbow section pressure loss measured 4–8 times greater than straight pipe sections across all tested conditions, with significantly higher growth rates. Rheological coefficients derived via linear fitting (R² ≥ 0.91) for straight pipes revealed an exponential increase with rising concentration (R² ≥ 0.91). Leveraging this exponential relationship, a predictive model for straight-pipe pressure loss was developed. Validation showed high accuracy, with absolute errors between predicted and experimental results ranging from 0.02% to 18.04%. The model was extended to predict pressure loss under broader operational parameters (concentration, flow rate, pipe diameter). Key simulations demonstrated that at 80% concentration and 2.8 m/s flow rate, increasing pipe diameter from 100 to 175 mm reduced pressure loss by approximately 50% and markedly decelerated its growth rate. Furthermore, pressure loss disparities between different flow velocities at identical concentrations diminished with larger diameters. These findings confirm that up-sizing pipe diameter effectively mitigates pressure losses induced by elevated mass concentration and flow velocity. For engineering applications, selecting larger pipelines enables simultaneous achievement of high flow rates and high concentrations during transport. The study establishes a reliable predictive framework and provides significant reference basis for optimizing the safe, efficient, and economical pipeline transport of modified backfill slurry in industrial settings.

Introduction

Coal mining, washing, and processing generate substantial amounts of coal gangue, accounting for approximately 10–20% of raw coal production^1–3. This massive volume of gangue occupies significant land resources, severely pollutes water sources, releases large quantities of CO₂ exacerbating the greenhouse effect, causes heavy metal contamination, and poses risks of spontaneous combustion and landslides^4,5. As the largest category of coal-based solid waste, the multifaceted problems caused by coal gangue urgently demand solutions. Backfill mining presents a crucial pathway for the large-scale utilization of coal gangue, effective mitigation of mining-induced damage, and improved coal resource recovery rates⁶. Accurately predicting the transportation characteristics of backfill slurries provides essential guidance for optimizing filling slurry transportation efficiencies^7–11.

Cementitious materials primarily serve to bind the backfill aggregates¹². However, Portland cement-based binders account for approximately 70% of the total backfill material cost, significantly hindering the broader adoption of backfill technology¹³. Using Portland cement is not only expensive, but its production also consumes substantial amounts of coal and limestone resources while emitting large quantities of CO₂. Thus, while addressing goaf stability and improving coal recovery, it introduces new resource and environmental challenges, conflicting with the national principles of ‘green development’ and the concept that ‘lucid waters and lush mountains are invaluable assets’. To address the issues associated with Portland cement in mine backfilling and better realize the goals of ‘treating waste with waste’, ‘mitigating mining impacts with waste’, and ‘green mining’ for sustainable mine development, researchers have explored using waste materials like coal gangue, fly ash, and coal gasification slag (CGS), combined with water, to form coal gangue slurries for goaf filling^14–16. Nevertheless, the chemical composition of CGS and fly ash is highly variable due to factors like raw coal constituents, additives, and processing techniques^15,16, leading to significant fluctuations in their properties and generally low reactivity, which limits their large-scale utilization in backfilling. Furthermore, the pursuit of sustainable mining practices has spurred interest in developing alternative, low-carbon binders from industrial solid wastes. This approach of waste valorization not only mitigates environmental hazards but also contributes to a circular economy. Significant research has been devoted to utilizing various industrial by-products, such as metakaolin¹⁷, slag¹⁸, and more recently, magnesium-based materials¹⁹, for creating sustainable construction materials.

Compared to binders like Portland cement, fly ash, and CGS, modified magnesium slag-fly ash (MMS-FA) cementitious material offers a low-cost, high-flowability, and excellent binding alternative composed entirely of solid wastes. MMS-FA binder is a hydraulic cementitious material prepared by activating and modifying slag from magnesium metal smelting and combining it with coal-based solid wastes like fly ash and CGS²⁰. Research has demonstrated that MMS-FA possesses cement-like binding properties and has been successfully applied for underground backfilling in mines such as Mahuangliang, Changxing, and Jinniu in Yulin, achieving full solid-waste backfilling with good results and meeting environmental requirements²¹. Liu et al.²² used modified magnesium slag and high-calcium fly ash as binder mixed with aeolian sand to create paste backfill, studying its rheological and mechanical properties. Sun et al.²³ prepared mine backfill binder by blending modified magnesium slag with fly ash, determining the optimal mass ratio; fly ash addition effectively enhanced strength, shortened hydration time, and increased hydration rate. Yang et al.²⁴ used modified magnesium slag as the primary binder, supplemented by fly ash, desulfurization gypsum, and CGS, to prepare backfill material, investigating its fluidity and strength characteristics; the results showed it met mine backfill requirements. Ruan et al.²⁵ studied the mechanical properties of MMS-FA cemented aeolian sand backfill, identifying an optimal mass ratio for the components. Numerous other researchers have extensively investigated the hydration and cementitious properties of modified magnesium slag itself and blends where it is the main binder supplemented by auxiliary materials (e.g., fly ash, CGS, gypsum), as well as the rheological and mechanical properties of backfill materials using modified magnesium slag to bind aggregates^26–28. Collectively, these studies elucidate the hydration mechanisms, flow behavior, and strength development of modified magnesium slag and the backfill materials derived from it.

However, existing research primarily focuses on applications requiring high strength, such as strip filling. For example, reference²¹ reports that backfill material prepared from MMS-FA binder and aeolian sand met the strength requirements for narrow strip paste filling in Mahuangliang Mine (≥ 4.9 MPa) and paste filling in Yuyang Mine (4.2–5.1 MPa), necessitating a minimum binder dosage as high as 30%. Using such high binder dosages to fill low-strength-requirement zones like the caving zone of a goaf is not only costly but also wasteful. For grouting backfilling in the caving zone where strength requirements are lower, the goal is to minimize binder addition while still meeting reinforcement needs. Current understanding of the transport characteristics of modified backfill slurry (a slurry prepared with a modified magnesium slag-fly ash binder and coal gangue aggregate) remains notably inadequate. Crucially, there is a lack of reported research on the pipeline transport characteristics of modified backfill slurry based on loop-pipe testing.

To facilitate the effective application of modified backfill slurry for grouting into the caving zone of goafs with lower strength requirements, it is essential to clarify its pipeline transportation behavior with low binder content. This study prepared modified backfill slurries at five different mass concentrations using MMS-FA binder and coal gangue. Loop-pipe tests were conducted at four flow velocities. Based on the test results, the influence patterns of mass concentration and flow velocity on the slurry’s transportation characteristics were elucidated. Experimental data were fitted to derive a suitable rheological model for characterizing the modified fill slurry. This model was then used to predict the pressure losses under various transport conditions, providing vital reference information for achieving the safe, efficient, and economical pipeline transport of modified backfill slurry.

Materials, schemes and systems

Experimental materials

The modified backfill slurry was prepared by mixing the modified magnesium slag-fly ash (MMS-FA) cementitious material with coal gangue of a specific particle size gradation and a defined quantity of tap water. The MMS-FA binder and the coal gangue used are shown in Fig. 1.

Fig. 1.

SEM and XRD testing of coal gangue and modified magnesium-coal based cementitious material.

The MMS-FA binder consists of modified magnesium slag (MMS) and fly ash (FA). The modified magnesium slag was obtained by activating and modifying raw magnesium slag generated during magnesium production at a magnesium plant in Yulin City, Shaanxi Province. The microstructure and phase composition of the modified magnesium slag were characterized using a German ZEISS Sigma 300 scanning electron microscope (SEM) and X-ray diffraction (XRD), respectively. Results, presented in Fig. 2a, b, show that the MMS-FA microstructure exhibits rod-like, flaky, and fragmented structures. To move beyond qualitative description, the porosity features in the SEM images were analyzed using ImageJ software, the pores distribution and statistical results of the SEM images of modified magnesium are show in Fig. 3. The analysis of multiple images indicates that the sample with MMS-FA binder has an average pore area of 0.07 μm², a total pore area of 5.86 μm², a min and max pore area of 0.1 μm² and 1.70 μm², respectively. Furthermore, the pore size distribution is narrower, with over 94% of the pores being smaller than 0.2 μm². The primary phase identified was β-C₂S, along with minor amounts of γ-C₂S, MgO, and CaO. The XRD patterns were further analyzed by comparing the relative intensity ratios of key peaks to semi-quantitatively assess phase changes. The intensity of the main β-C₂S peak (around 32.6° 2θ) is 1.5 times as much as γ-C₂S peak (around 32.2° 2θ), is 2.8 times as much as MgO peak (around 41.3° 2θ), is 6.6 times as much as CgO peak (around 37.4° 2θ). This indicates a substantial increase in β-C₂S formation, which will effectively enhanced the hydration activity of the MMS-FA²³.

Fig. 2.

SEM image and XRD phase composition of modified magnesium slag.

Fig. 3.

The pores distribution and statistical results of the SEM images of modified magnesium slag.

Chemical composition analysis via X-ray fluorescence (XRF) spectrometry revealed that the main constituents of the MMS are SiO₂ (19.12%), CaO (40.82%), Al₂O₃ (1.40%), MgO (3.49%), Fe₂O₃ (2.55%), and SO₃ (0.05%). The primary components of the magnesium slag are similar to those of Portland cement clinker, endowing it with inherent hydration activity.

The modified magnesium slag (MMS) and fly ash (FA) were uniformly mixed at the optimal ratio of 4:1 by mass²³. This mixture was processed through a crusher and subsequently ground in a ball mill within the cement production system of a cement plant in Yulin City to obtain the modified magnesium slag-fly ash (MMS-FA) cementitious material powder, achieving a particle size comparable to that of cement. Particle size distribution analysis using a laser particle size analyzer is shown in Fig. 4a. The particle size ranges from 0.1 μm to 275 μm, with the majority falling between 0.1 μm and 138 μm.

Fig. 4.

Particle sizes and grading curves of MMS-FA cementitious material and coal gangue aggregates.

The coal gangue used in this study, totaling 5 tonnes, was sourced from Liangshuijing Coal Mine in Yulin City, Shaanxi Province. Analysis of representative samples indicated that the as-received gangue particles varied in size from powder-like fragments up to 100 mm, primarily consisting of mudstone. The average density of the gangue, determined using the wax-sealing method, was 2.51 g/cm³. The average moisture content, measured by the oven-drying method, was 7.45%. Due to the excessively large particle size of the raw gangue, which made it unsuitable for direct slurry preparation, the material was processed using a high-fineness crusher (Model: 2PC800 × 700) for size reduction. The crushed gangue was then sieved through a 3 mm mesh screen. Gangue particles passing the 3 mm sieve were used as the aggregate for preparing the modified backfill slurry. The particle size distribution (gradation) of this < 3 mm gangue aggregate was determined, and the results for mass percentage and cumulative mass percentage are presented in Fig. 4b.

Test schemes

While ensuring the modified backfill slurry meets the requirements for safe and efficient pipeline transport, the proportioning design aims to maximize the disposal of coal gangue. To achieve this, the addition of the modified magnesium slag-fly ash (MMS-FA) cementitious material should be minimized, while simultaneously increasing the mass concentration of the slurry. The preparation procedure for the modified backfill slurry is illustrated in Fig. 5.

Fig. 5.

Preparation process of the modified backfill slurry.

To determine the appropriate dosage of Modified Magnesium Slag-Fly Ash (MMS-FA) binder, slurries with water-to-binder ratios of 100:1, 100:2, and 100:3 were prepared. The rheological parameters of these three slurry mixes were tested, and the results are summarized in Table 1.

Table 1.

Viscosity coefficient and slumps of filling slurry with different binder dosages.

Dosage/%	Yield stress/Pa	Apparent viscosity/Pa s	Fluidity index	R2
1%	21.52	0.0021	2.441	0.997
2%	23.61	0.0027	2.379	0.999
3%	26.68	0.0040	2.206	0.999

According to Table 1, when the water-to-binder ratio increased from 100:1 to 100:2, the yield stress increased by 2.1 Pa, the apparent viscosity increased by 0.0006 Pa s, and the fluidity index decreased by 0.07. When the ratio further increased from 100:2 to 100:3, the yield stress increased by 3.1 Pa, the apparent viscosity increased by 0.002 Pa s, and the fluidity index decreased by 0.17. These results indicate that the changes in rheological parameters were significantly more pronounced when the water-to-binder ratio increased from 100:2 to 100:3 compared to the change from 100:1 to 100:2.

The grouting backfill slurry studied in this work is mainly used to fill the pores and fractures between the caved rock and the fractured zone in the goaf. Its primary function is to densify these voids and fractures, with an additional important objective being the increased disposal of gangue. The key operational requirement is that the slurry must be pumpable. Relevant research findings indicate that even non-cemented or weakly cemented pure gangue slurries can effectively control the deformation of overlying strata when used to fill the pores and fractures in the goaf. For example, as referenced in the manuscript, Literature²⁹ used a gangue slurry with a mass concentration of 65% (composed only of gangue and water) for grouting into the goaf, which significantly improved the stability of the overlying strata. Furthermore, several other studies have investigated the use of weakly cemented materials for grouting reinforcement of caved and fractured rock masses. Results demonstrate that even materials with very low cementitious strength provide effective control over overlying strata deformation. For instance ³⁰, and Literature³¹ respectively studied the reinforcement of caved rock masses using fly ash slurry and fly ash-gasification slag cemented gangue slurry.

Considering the relatively high cost of cementitious materials, employing a lower binder dosage—while still meeting the essential backfill requirements—not only substantially reduces backfill costs but also allows for the disposal of a larger quantity of gangue. Therefore, the selected MMS-FA dosage of 2% is justified and sufficient to meet the backfill objectives.

When the mass concentration of the modified backfill slurry exceeded 72%, slump tests conducted according to the Chinese Standard GB/T 50080-2016 (Standard for test method of performance of ordinary concrete mixtures) revealed a slump less than 250 mm using a standard slump cone (top diameter of 100 mm, bottom diameter of 200 mm, height of 300 mm). At this concentration, slurry mixing became difficult, and the required pumping pressure exceeded 80% of the rated pump pressure (16 MPa) within a pipeline of 125 mm internal diameter and 150 m length.

To ensure the smooth execution of the loop-pipe tests, stable slurry transport, and adequate flow spread, the initial mass concentration for the loop-pipe test slurries was set at 72% with the MMS-FA binder dosage maintained at 2% of the gangue aggregate mass. The ‘mass concentration’ of the slurry is defined as the percentage of the total mass of solids (including both the binder and the coal gangue aggregate) to the total mass of the mixture. All slurries were prepared in a mixer with a capacity of 3 m³. Preliminary tests confirmed that 10 min of mixing produced a uniformly blended slurry; therefore, the mixing time for all slurries was controlled at 10 min. To investigate the applicability over a wider range, slurries were prepared at five different mass concentrations: 72%, 70%, 68%, 66%, and 64%.

Concurrently, for comparative validation of the rheological advantages of the modified slurry, a control slurry was prepared using Type 42.5 Portland cement instead of the MMS-FA binder. This cement-gangue slurry was prepared at a mass concentration of 64%, maintaining an identical mix proportion (i.e., cement dosage = 2% of gangue mass, water content equivalent to the modified slurry at 64% concentration). Loop-pipe testing was also performed on this cement-gangue slurry to characterize its rheological properties. In the subsequent results analysis, this cement-gangue slurry test group is denoted as C. Specifically, C(64) or C(64%) refers to the cement-gangue slurry with a 64% mass concentration. The detailed mix proportions for all slurries are provided in Table 2. Note: Water-to-solid ratio is defined as the mass ratio of added water to total solid materials (the sum of gangue aggregate and cementitious material). Binder-to-aggregate ratio is the mass ratio of cementitious material to gangue aggregate.

Table 2.

The experimental proportions of the modification filling slurry.

Mass concentration/%	Water-to-solid ratio	Binder-to-aggregate ratio/%
C(64)	18:32	1:49
64	18:32	1:49
66	17:33	1:49
68	16:34	1:49
70	15:35	1:49
72	14:36	1:49

To prevent pipeline blockage caused by the sedimentation of solid particles within the backfill slurry and to maintain a uniformly suspended mixture, it is essential to determine the critical flow velocity for the slurry. A commonly employed method for determining this critical velocity is as follows³²:

1

where U_kp is the critical flow velocity (m/s); ρ_s is the density of the coal gangue slurry (kg/m³); ρ_h is the density of tap water (kg/m³), conventionally taken as 1000 kg/m³; C_QV is the solid volume fraction in the slurry, calculated as the total slurry volume per unit volume minus the water volume; D is the pipe internal diameter (m), specified as 0.125 m in this study. The measured densities of the modified backfill slurries at mass concentrations of 72%, 70%, 68%, 66%, and 64% were 1600 kg/m³, 1568 kg/m³, 1537 kg/m³, 1506 kg/m³, and 1476 kg/m³, respectively. Using Eq. (1), the critical flow velocities for the five modified backfill slurries at different mass concentrations were calculated. The results are presented in Table 3. Based on the calculated critical flow velocities (U_kp) for the modified backfill slurries presented in Table 3, the critical velocity was found to be slightly above 1.0 m/s. To ensure the test flow velocities provided broad coverage of potential operating conditions, the minimum flow velocity for the loop-pipe tests was set at 1.0 m/s.

Table 3.

The critical velocity of the modification filling slurry.

Volume fraction/%	Density/kg/m3	Critical flow velocity/m/s
55	1600	1.15
53	1568	1.14
51	1537	1.13
49	1506	1.12
47	1476	1.11

Simultaneously, considering that higher conveying rates might be required under different backfill operating conditions, the maximum flow velocity was determined based on velocity ranges reported in previous loop-pipe studies³³. Finally, the maximum flow velocity was set at 2.7 m/s. The selected velocity range (1.0–2.7 m/s) is considered sufficient to meet the requirements of typical backfill engineering applications. To account for varying velocity demands across different backfill projects, loop-pipe tests were conducted for each mass concentration at four distinct flow velocities: 1.0, 1.6, 2.2, and 2.7 m/s.

The testing sequence was as follows:

1. The initial loop-pipe test commenced with the modified backfill slurry at a mass concentration of 72% and a flow velocity of 1.0 m/s.

2. After the slurry flow stabilized, the pressure generated by the slurry was monitored using pressure sensors for a duration of 5 min.

3. The flow velocity was then sequentially increased to 1.6 m/s, 2.2 m/s, and finally 2.7 m/s. For each velocity step, the slurry was circulated through the loop twice, with pressure data recorded for 5 min after stabilization during each circulation.

4. Following the tests at 72% concentration, tap water was added to adjust the slurry mass concentration down to 68%.

5. The loop-pipe test procedure (steps 1–3) was repeated for this 68% concentration slurry at the same four flow velocities (1.0, 1.6, 2.2, 2.7 m/s).

6. This process of reducing the concentration (by adding water) and repeating the four-velocity test sequence was continued sequentially for concentrations of 66% and finally 64%.

7. The loop-pipe testing concluded after completing the tests for all four flow velocities at the final concentration of 64%.

Test systems

The loop-pipe tests for the modified backfill slurry were conducted using a semi-industrial loop-pipe test system, as illustrated in Fig. 6.

Fig. 6.

Loop test system.

The system comprised the following key components:

Industrial pump

One HGBSQ120-18-630 model piston-type industrial slurry pump, with a pumping pressure range of 0-–16 MPa.

Loop pipeline

Constructed from 16Mn (Q355B) wear-resistant seamless steel pipe. The total pipeline length was approximately 150 m, with an internal diameter of 125 mm and a wall thickness of 14 mm.

Pressure sensors

Three ZPM317 model flush diaphragm pressure sensors. Prior to testing, these sensors were calibrated using a hydraulic oil pressure method. The sensor heads were placed within a hydraulic oil chamber. The oil pressure was incrementally increased from 0 to 16 MPa in steps of 0.1 MPa. At each pressure step, the sensor output was adjusted to match the applied oil pressure. Calibration was completed once the final pressure reading stabilized at 16 MPa after reaching the maximum pressure.

Data acquisition

One MultiSystem 5060 hydraulic multimeter measurement device was used to record data from the pressure sensors.

Flow meter

An LDG-SUP electromagnetic flow meter installed on the pipeline to monitor the slurry flow rate (volume flow), with an accuracy of ± 0.5%.

Pressure monitoring points

Three ZPM317 flush diaphragm pressure sensors (P1, P2, P3), each with an accuracy of ± 0.1% and a range of 0–30 MPa, were installed on the pipeline to monitor the pressure exerted by the slurry on the pipe wall during circulation. The straight pipe section between sensors P1 and P2 was 50.6 m long, and the bent pipe section between sensors P2 and P3 was 4.2 m long (refer to Fig. 6 for locations).

Modified backfill slurry, mixed in the agitator, was pumped by the industrial slurry pump into the loop pipeline and subsequently returned to the collection tank.

Determination of pressure loss

During pipeline transport, the backfill slurry exerts pressure on the pipe walls. This pressure data is fundamental for determining the pressure loss (head loss) along the pipeline, providing the basis for specifying required pump pressure.From the pressure versus pumping time curves recorded during the loop-pipe tests, the mean value of all pressure peaks corresponding to the stable flow regime was calculated for each mass concentration and flow velocity. This yielded the pressure exerted by the modified backfill slurry on the pipe wall at measurement points P1, P2, and P3. The pressure difference (ΔP) was then calculated between adjacent sensor pairs: between P1 and P2 (ΔP_P1-P2) and between P2 and P3 (ΔP_P2-P3).Combining these pressure differences with the known distances (l) between the sensor pairs (50.6 m between P1-P2 and 4.2 m between P2-P3), the unit-distance pressure drop (pressure loss per meter, ΔP/l) was calculated. The calculation method is as follows:

2

where, i is the pressure loss per kilometer (MPa/km); ΔP is the pressure difference between the two measurement points (MPa); l is the distance between the two measurement points (km).

Experimental results

Loop pipe pressures

Due to the large volume of loop-pipe test data, representative results are presented for clarity. Figure 7 shows the variation of loop-pipe pressure with pumping time over the 250–300 s interval for the modified backfill slurry at a flow velocity of 1.6 m/s and across all five mass concentrations.

Fig. 7.

Pressure–time curves of the modification filling slurry with five mass concentrations as a flow rate of 1.6 m/s in loop test.

As evident from Fig. 7, the pressure at each measurement point exhibits periodic fluctuations during slurry circulation. This phenomenon arises from the use of a plunger pump for slurry delivery. This pump operates by the rapid reciprocating motion of plungers within cylinders, causing cyclic changes in the volume of the sealed working chambers. This action induces a pulsating flow of the modified slurry within the loop, consequently generating periodic pressure variations. While the pump is the primary cause of the fluctuations, effects like particle migration and thixotropy may also play a role in the overall flow resistance and pressure profile. Furthermore, the loop-pipe pressure gradually decreases along the flow direction as the transportation distance of the slurry increases. Critically, the loop-pipe pressure increases significantly with higher slurry mass concentration. When the mass concentration was raised from 64 to 72%, the pressure at measurement point P1 increased by approximately 36%, the pressure at measurement point P2 increased by approximately 34%, the pressure at measurement point P3 increased by approximately 27%.

Loop pipe pressure loss

The pressure loss for both the cement-gangue slurry and the modified backfill slurry under various flow velocities and mass concentrations within the straight pipe sections of the loop system was calculated using Eq. (2). The results are presented in Fig. 8. Comparison with modified backfill slurry, at a mass concentration of 64%, the cement-gangue slurry exhibits a higher pressure loss. Furthermore, as the flow velocity increased, the pressure loss of the cement-gangue slurry increased at a faster rate. This indicates that, under identical operating conditions, the modified backfill slurry requires lower pumping pressure and is easier to transport.

Fig. 8.

Variation of pressure loss of straight and elbow sections under different flow velocities.

For the modified backfill slurry, the pressure loss in both the straight and bent pipe sections increased progressively with higher flow velocities. This increase is attributed to the elevated internal friction within the slurry at higher velocities, requiring greater energy to overcome the pressure loss exerted by the pipe walls.

Across all tested flow velocities, the pressure loss within the bent pipe section was significantly higher than in the straight section. Specifically, the pressure loss in the bends was approximately 4 to 8 times greater than in the straight pipes. This substantial difference stems primarily from the centrifugal forces acting on the slurry flow within the bends, generating considerably higher pressure losses. A strong linear relationship was observed between the flow velocity and the pressure loss for the modified backfill slurry.

At 64% mass concentration, increasing the velocity from 1.0 m/s to 2.7 m/s resulted in an increase in pressure loss of approximately 16.8% in the straight pipe section, while the increase in the bent section was significantly higher, reaching approximately 83.4%. At the higher concentration of 72%, the same velocity increase (1.0 m/s to 2.7 m/s) caused an increase of approximately 24.7% in the straight section pressure loss and approximately 54.6% in the bent section.

The pressure loss for both the cement-gangue slurry and the modified backfill slurry under various flow velocities and mass concentrations within the bent pipe sections of the loop system was calculated using Eq. (2). The results are presented in Fig. 9.

Fig. 9.

Variation of pressure loss of straight and elbow sections under different mass concentrations.

Analysis of Fig. 9 reveals that the pressure loss in both the straight and bent pipe sections increases progressively with higher mass concentration of the modified backfill slurry. However, this increase exhibits a distinct non-linear trend. This non-linear behavior is attributed to the higher concentration of solid particles. As concentration increases, the frequency of particle–particle interactions (collisions and squeezing) within the slurry intensifies. More energy is consumed by friction between the solid particles themselves. The friction between the slurry and the inner pipe wall increases significantly. Collectively, these effects lead to the observed rise in pressure loss. Furthermore, both the magnitude of the pressure loss and its rate of increase with concentration are substantially greater within the bent sections compared to the straight sections. The effect of concentration is markedly more pronounced in the bends. This enhanced sensitivity arises from fundamental flow differences, in the straight pipes, the flow regime is relatively stable, approaching laminar flow conditions. Consequently, the friction between the slurry and the pipe wall is lower. In the bent sections, centrifugal forces act on the flowing slurry, significantly amplifying the friction and resulting in considerably higher pressure losses. The significantly elevated pressure loss in the bends are attributed to the complex flow dynamics, pressure gradients develop across the bend, pressure decreases along the inner bend while increasing along the outer bend³⁴. This pressure differential increases the internal frictional pressure loss within the slurry. Centrifugal forces act on the slurry, causing aggregates to migrate toward the outer bend. Consequently, the solid concentration becomes higher near the outer bend wall compared to the inner wall. The combined effect of increased internal friction and localized higher solids concentration near the outer wall^35,36.

At a flow velocity of 1.0 m/s, increasing the mass concentration from 64 to 72%, raised the straight section pressure loss from 2.86 MPa/km to 6.40 MPa/km (an increase of approximately 123.8%), raised the bent section pressure loss from 13.60 MPa/km to 33.00 MPa/km (an increase of approximately 142.6%). At a higher flow velocity of 2.7 m/s, increasing the concentration from 64 to 72% raised the straight section pressure loss from 3.34 MPa/km to 7.98 MPa/km (an increase of approximately 138.9%), raised the bent section pressure loss from 24.94 MPa/km to 51.03 MPa/km (an increase of approximately 104.6%).

In order to quantitatively analyze the influence of mass concentration on the resistance along the pipeline, scatter plots of the resistance along the pipeline under different mass concentrations and flow rates were drawn, and they were fitted. The fitting results are presented in Table 4, where c_w represents mass concentration. The results show that the pressure loss along the pipeline can be described by an exponential function with the mass concentration, and the fitting degree is between 0.94 and 0.99.

Table 4.

The fitted results between the pressure loss and mass concentration.

Velocity/m/s	Straight section		Bent section
	Fitted results	R2	Fitted results	R2
1.0		0.99		0.98
1.6		0.99		0.94
2.2		0.99		0.99
2.7		0.99		0.99

These results demonstrate that increasing the flow velocity leads to higher pressure losses during pipeline transport of the modified backfill slurry. Critically, the pressure loss and its rate of increase with velocity are substantially greater within bent pipe sections compared to straight sections. The pressure loss exhibits an approximately linear increase with flow velocity.

Rheological parameters calculation

Yield stress and plastic viscosity are two critical rheological parameters governing the flow behavior of backfill slurries^37,38. The rheological parameters are fundamental properties that characterize the intrinsic flow behavior of a backfill slurry. In theory, once the slurry composition is fixed, these parameters are considered constants, independent of external flow conditions³⁹. Selecting an appropriate rheological model is paramount for accurately determining these parameters, and the suitability of the chosen model directly impacts the precision of pressure loss predictions⁴⁰. Rheometric tests and loop-pipe tests represent the primary methods for determining rheological parameters. However, existing research indicates that parameters derived from rheometric tests often exceed those obtained from loop-pipe tests, leading to an overestimation of rheological properties. In contrast, results based on loop-pipe testing provide a more realistic reflection of the slurry’s rheological behavior under actual pipeline flow conditions⁴¹. During pipeline transport, modified backfill slurries can be effectively modeled as Bingham plastic fluids. This classification is supported by two key characteristics observed in pipeline flow: the pressure loss exhibits a distinct linear relationship with flow velocity. The flow regime predominantly manifests as laminar flow^42,43. Consequently, the Bingham plastic model is well-suited for characterizing the rheological behavior of backfill slurries in pipeline transportation³⁴. As evidenced by the data presented in Fig. 7, the modified backfill slurry demonstrates a clear linear relationship between pressure loss and flow velocity within the straight pipe section. This behavior aligns precisely with the defining characteristic of a Bingham plastic fluid. Therefore, the Bingham plastic model was selected to describe the rheological properties of the modified slurry. This model is defined by two intrinsic parameters, the yield stress and the plastic viscosity⁴⁴. The relationship between the pressure loss during pipeline transport of the modified slurry and its Bingham rheological parameters can be characterized using the Buckingham equation⁴⁵:

3

where, τ_w is the shear stress, Pa; τ₀ is the yield stress, Pa; η is the plastic viscosity, Pa·s; D is the inner diameter of the loop pipe, m; v is the flow velocity, m/s.

Based on the force analysis of backfill slurry during pipeline transport , the pressure loss encountered by the slurry within the pipeline is numerically equal to the wall shear stress generated during slurry flow³⁵:

4

where i is the pressure loss, MPa/km, which can be calculated using Eq. (2).

By combining Eqs. (3) and (4), the expression for the pressure loss during pipeline transport of the modified backfill slurry can be derived⁴⁵:

5

Given the linear relationship between the pressure loss and the slurry flow velocity, Eq. (5) can be expressed in the following functional form:

6

where , .

Leveraging the established linear relationship between pressure loss and flow velocity for the modified backfill slurry in straight pipe section, Eq. (6) was employed to fit the pressure loss data obtained from the loop-pipe tests for both the cement-gangue slurry and the modified slurry across the tested velocities. The fitting results are presented in Fig. 10, and the corresponding fitting equations are summarized in Table 5.

Fig. 10.

Fitting results of pressure loss in straight and bend pipe sections fitted by the Bingham plastic model under different flow velocities.

Table 5.

Rheological parameters of the modification filling slurry fitted by the Bingham plastic model.

Concentration/%	Fitted function	R2	τ0/Pa	η/Pa S
C64	i = 0.44v + 2.55	0.96	59.766	0.215
64	i = 0.15v + 2.73	0.95	63.984	0.073
66	i = 0.21v + 2.92	0.97	68.438	0.103
68	i = 0.30v + 3.27	0.92	76.641	0.147
70	i = 0.36v + 4.25	0.91	99.609	0.176
72	i = 0.51v + 6.01	0.95	140.859	0.249

Analysis of the fitting results reveals an excellent linear correlation between pressure loss and velocity for both slurry types. The coefficient of determination for all fits exceeded 0.91, confirming the strong linear trend. This high degree of fit provides reliable rheological parameters for subsequent pressure loss calculations.

By combining the fitting equations shown in Table 5 with the definitions of coefficients a and b in Eq. (6), the yield stress and plastic viscosity for both the cement-gangue slurry and the modified backfill slurry in the straight and bent sections were determined. These calculated rheological parameters are also presented in Table 5.

Comparison at 64% mass concentration, the cement-gangue slurry exhibited a slightly lower yield stress but a plastic viscosity approximately three times higher than the modified slurry, this demonstrates that utilizing the MMS-FA binder significantly enhances the flowability of the gangue slurry compared to Portland cement. Increasing the mass concentration of the modified slurry led to increases in both the yield stress and plastic viscosity. Table 5 clearly indicates a strong dependence of the modified slurry’s rheological parameters on mass concentration. Analyzing the quantitative relationship between these parameters and concentration will provide a valuable basis for predicting pipeline pressure losses under various conditions.

It is important to note that the significantly higher pressure losses observed in the bend sections are primarily due to complex fluid dynamic phenomena, including secondary flows and particle migration, rather than an increase in the intrinsic rheological properties of the slurry. Consequently, the Bingham model, which is validated for straight-pipe laminar flow, is not applied to these sections.

Loop pipe pressure loss fitting model

The pressure loss of backfill slurry serves as a key basis for backfill system design and equipment selection. Predicting this pressure loss under various operating conditions based on experimental results provides crucial guidance for optimizing material mix proportions, selecting pipeline specifications, determining pumping capacity requirements, and designing other aspects of the backfill system. As shown in Table 5, the rheological parameters of the modified backfill slurry exhibit a distinct correlation with mass concentration. For the straight pipe section, the variation of both yield stress and plastic viscosity with mass concentration displays a clear exponential trend. Exponential functions were fitted to the yield stress and viscosity data from Table 5 for different concentrations. The results, presented in Fig. 11, show excellent fits, cefficient of determination (R² = 0.91) for yield stress, coefficient of determination (R² = 0.99) for plastic viscosity. This high goodness-of-fit confirms that exponential functions effectively characterize the variation of yield stress and plastic viscosity with concentration in straight pipes. For the bent pipe section, however, the flow behavior and resulting rheology are significantly more complex than in straight pipes. Consequently, the correlation between rheological parameters, yield stress and plastic viscosity, and mass concentration is weaker. Based on the current experimental results, no clear correspondence could be established. A more systematic investigation specifically targeting bend rheology is required to develop predictive relationships for bent sections. Furthermore, the length of the elbow pipe is very short compared to the total length of the filling pipeline. Therefore, more attention should be paid to the flow state of the slurry in the elbow section. Therefore, the subsequent discussion focuses solely on the predictive model and results for frictional pressure loss in straight pipe sections for the modified backfill slurry.

Fig. 11.

The fitting results of rheological parameters of the modification filling slurry with different mass concentrations.

Based on the fitting results presented in Fig. 11, the relationship between the rheological parameters of the modified backfill slurry and mass concentration can be quantitatively expressed as follows:

7

where c_w is the mass concentration, %.

Based on the established correspondence between the rheological parameters of the modified backfill slurry and its mass concentration, the rheological parameter relationships from Eq. (7) for different concentrations can be substituted into Eq. (5). This yields a practical predictive formula for the pressure loss of the modified slurry, expressed solely in terms of flow velocity and mass concentration:

8

To verify the reliability of the proposed model, additional loop-pipe tests were conducted to measure the pressure loss for modified backfill slurries at mass concentrations of 62% and 74%. Concurrently, Eq. (8) was used to calculate the pressure loss for the slurry across four flow velocities and seven mass concentrations (including the original five and these two new concentrations). A comparison of the calculated and experimentally measured pressure losses is presented in Fig. 12.

Fig. 12.

Comparison between the calculation results and the test results for the pressure loss.

Analysis of Fig. 12 reveals that the pressure losses calculated using the proposed model for the modified slurry exhibit excellent agreement with the experimental measurements across all four velocities and seven concentrations, both in terms of magnitude and variation trend. The absolute error between calculated and measured pressure losses ranged from 0.02% to 18.04%. Detailed error analysis shows, tt 1.0 m/s velocity, errors ranged from 0.99% to 13.37% as concentration increased from 62 to 74%. At 2.7 m/s velocity, errors ranged from 0.02% to 18.04% as concentration increased from 64 to 74%. At 62% concentration, errors ranged from 16.63% to 17.82% as velocity increased from 1.0 m/s to 2.7 m/s. At 74% concentration errors ranged from 9.17% to 14.24% as velocity increased from 1.0 m/s to 2.7 m/s. Overall, the pressure losses calculated by the proposed formula for the modified slurry across the seven concentrations and four flow velocities demonstrate high accuracy compared to experimental results. The model reliably predicts the pressure loss in straight pipe sections under varying conveying velocities and mass concentrations. It thus provides a robust computational tool for predicting pipeline pressure loss during the transport of modified backfill slurry.

Parameter sensitivity analysis

Parameter sensitivity analysis provides an intuitive understanding of how pressure loss varies under the influence of different operational and design parameters. To facilitate the practical application of the modified backfill slurry in real-world backfill engineering and meet diverse design requirements, the proposed pressure loss calculation model (Eq. 8) was employed to conduct a parameter sensitivity analysis. The analysis evaluated the pressure loss under the following conditions: mass concentration ranging from 60 to 80%, in increments of 2%; flow velocity ranging from 0.8 m/s to 2.8 m/s, in increments of 0.4 m/s; pipe inner diameter include four diameters commonly used in backfill engineering, 100, 125, 150, and 175 mm.

The predicted pressure losses are presented in Fig. 13. For identical mass concentration and flow velocity, the pressure loss decreases significantly as the pipe diameter increases, larger pipe inner diameters result in smaller differences in pressure loss between different flow velocities and a reduced rate of increase in pressure loss with increasing velocity. Similarly, larger pipe inner diameters diminish the impact of mass concentration on the pressure loss.

Fig. 13.

Prediction results of the pressure loss of modified backfill slurry with mass concentrations and flow rates under 4 kinds of pipe diameters.

Building upon the results in Figs. 13 and 14 illustrates the combined effect of mass concentration, flow velocity, and pipe diameter on pressure loss. First, variation of pressure loss with mass concentration (60% to 80%) at a low velocity (0.8 m/s) and small diameter (100 mm). Second, variation of pressure loss with flow velocity (0.8 m/s to 2.8 m/s) at a high concentration (80%) and the small diameter (100 mm). Third, variation of pressure loss with pipe diameter (100 mm to 175 mm) at the high concentration (80%) and high velocity (2.8 m/s). Analysis of Fig. 14 reveals that increasing the pipe diameter effectively mitigates the high pressure losses induced by high concentrations and high velocities, achieving a reduction of approximately 50%. Therefore, where site conditions permit, selecting larger pipe diameters is highly advantageous. This approach facilitates the use of higher slurry velocities and mass concentrations, optimizing transport efficiency and capacity.

Fig. 14.

Variation laws of the pressure loss under the influence of single factor superposition.

While a larger diameter pipe reduces frictional head loss and lowers long-term pumping costs (operational expenditure), it incurs a higher initial capital investment. This includes the cost of the pipe itself, which increases more than linearly with diameter, as well as higher costs for associated supports, valves, and installation labor, especially in the constrained spaces of an underground mine. The installation of large-diameter pipes is often constrained by the cross-sectional dimensions of underground drifts and shafts. Using a pipe that is too large can compromise the safe passage of personnel and equipment, and limit space for other essential services (e.g., ventilation ducts, cables). Furthermore, handling, transporting, and installing heavier, bulkier pipes underground presents significant logistical challenges. A system designed with a single, large-diameter pipe may lack the operational flexibility of a multi-pipeline system. For instance, during maintenance or a blockage in a single large pipe, the entire production line might be shut down, whereas a system with multiple smaller lines could allow for continued operation at a reduced capacity. Therefore, the optimal pipe diameter is not solely determined by minimizing pressure loss, but by finding an economic balance that minimizes the total cost over the lifecycle of the pumping system, while adhering to the physical and operational constraints of the underground mining environment.

Conclusions

This study systematically investigated the pipeline transport characteristics of modified backfill slurry prepared with low-dosage (2 wt.%) modified magnesium slag-fly ash (MMS-FA) binder and coal gangue. Key findings and implications are summarized as follows:

1. The pressure loss of the modified backfill slurry exhibits a linear positive correlation with flow velocity, confirming its rheological behavior aligns with the Bingham plastic model. While pressure loss increases linearly with velocity, it demonstrates nonlinear growth with mass concentration. Critically, pressure loss in bent pipe sections is 4 to 8 times greater than in straight sections, with both magnitude and rate of increase being higher in bends. Consequently, optimizing bend section layout in slurry transport systems is strongly recommended.

2. The Bingham plastic model accurately characterized the relationship between pressure loss and flow velocity in both straight and bent pipes, yielding excellent fits (R² ≥ 0.91). Yield stress and plastic viscosity increase progressively with higher slurry mass concentration. For straight pipes, yield stress and plastic viscosity follow an exponential relationship with mass concentration.

3. The developed pressure loss calculation model, incorporating the quantitative relationships between rheological parameters and mass concentration, predicted pressure losses with high precision. The absolute error between predicted and experimentally measured values ranged from 0.02% to 18.04%. This verifies the model’s reliability for predicting pressure loss in straight pipes and provides a robust theoretical foundation for engineering design of modified slurry transport systems.

4. Parametric sensitive analysis using the pressure loss model across wide operational ranges—mass concentration (60–80%), flow velocity (0.8–2.8 m/s), and pipe diameter (100–175 mm)—yielded key design insights, increasing pipe inner diameter dramatically reduces pressure loss, larger pipe inner diameters attenuate the sensitivity of pressure loss to changes in velocity and concentration, resulting in smaller differences and lower growth rates of pressure loss across velocities at a given concentration. Prioritizing larger pipe inner diameters in engineering practice enables the simultaneous achievement of high flow velocity and high slurry concentration requirements.

Despite the valuable insights provided, this study has certain limitations that should be acknowledged. Firstly, the test loop incorporated a short elbow section, which may not fully capture the pressure loss and wear characteristics of more complex, real-world pipeline networks with multiple or longer bends. Secondly, the investigation focused on flow characteristics and did not evaluate the strength development of the backfill material over time, which is a critical parameter for its goaf support. Finally, the rheological analysis was conducted using a single binder dosage; therefore, the findings are specific to this mixture proportion and do not explore the optimization of binder content for economic or performance trade-offs. Future work will address these aspects by employing a more elaborate loop configuration, integrating strength development tests, and investigating the effect of varying binder dosages.

Author contributions

Zhizhen Liu: Methodology, Software, Experimental, Writing-original draft, Funding acquisition. Yi Jin: Supervision, Resources, Project administration. Hu Zhou: Writing—review & editing, Project administration. Lang Liu: Conceptualization, Resources, Project administration. Deyu Chong: Project administration, Experimental. Mengbo Zhu: Writing—review & editing, Project administration, Funding acquisition. Dongkui Li: Supervision, Resources, Experimental. Baoning Wei: Supervision, Resources. Jiangbo Wei: Supervision, Resources, Experimental. Jing Zhou: Supervision, Resources, Funding acquisition. Dengdeng Zhuang: Supervision, Resources, Funding acquisition. Wei Lin: Data curation.

Funding

This study was supported by the National Natural Science Foundation of China (Grant Nos. 52504145 and 52204175 and 52304152), the China Postdoctoral Science Foundation (Grant Nos. 2024MD753979 and 2024MD764016), and the Shaanxi Province Postdoctoral Science Foundation (Grant Nos. 2024BSHSDZZ210 and 2024BSHSDZZ195).

Data availability

All data and materials are available upon reasonable request from the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.